Cut-sets in infinite graphs and partial orders

Hajnal, A. and N. Sauer, Cut-sets in infinite graphs and partial orders. Discrete Mathematics 117 (1993) 113-125. The set S c V(U) is a cut-set of the vertex v of a graph 9 if v is not adjacent to any vertex in S and, for every maximal clique C of Q, ({v} u S) n C # 0. S is a cut-set of the element v of a partial order 9 if S is a cut-set of v in the comparability graph of 8. Given upper bounds for the clique sizes and cut-set sizes of g, we will determine the largest size of an independent set of vertices of Q. If 4 is the comparability graph of some partial order 9, we will also determine the best possible upper bounds for the size of a maximal antichain of 8.